Plate trick
In mathematics and physics, the plate trick, also known as Feynman's plate trick, Dirac's belt trick, spinor spanner or quaternionic handshake is any of several particular physical demonstrations of the mathematical theorem that SU(2) double-covers SO(3), or sometimes this fact itself. The usual demonstration, as indicated by the name, is to hold a plate on one's flat palm, then perform two subsequent rotations of the arm holding the plate which results in the original position.
Topologists usually call this the belt trick, although some knot theorists, such as Louis Kauffman have dubbed it the quaternionic handshake. The reference to quaternions is because the action of SU(2) considered as the unit quaternions, on the 2-sphere, considered as pure unit quaternions, gives the double covering.
The plate trick is the mathematical physics reason why particles in a four-dimensional spacetime are either fermions or bosons. See the Spin-statistics theorem for more details.
[edit] See also
[edit] External links
- Air on the Dirac Strings
- Animation of Dirac belt trick
- Video of Kauffman's quaternionic handshake
- Abstruse Goose Reference
- The Spinor Spanner The American Mathematical Monthly, Vol. 80, No. 9, Nov., 1973
